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I have been following the developments around the Shawyer EM drive for about 2 years now as NASA and other parties test it out in various environments. To preface, I would very much like to see the EM drive work so sorry in advance if I am afflicted with a case of confirmation bias.
The most recent test in Dresden, Germany (the paper by M. Tajmar et al.) to me seems like another test that proves this idea may have some validity. As you may know if you are thinking about answering this question, the main concern with this idea is that it violates the momentum conservation principle (i.e., there must be something else that is causing the "thrust" force the experimenters are observing).
At this point, I need to say my background in physics is only through quantum mechanics and special relativity. I have dabbled in General Relativity and Quantum Field Theory, but don't yet have the mathematical prowess to fully appreciate them. I am an engineer, not a physicist, so forgive me if my arguments are a bit flawed. That's why I'm asking after all!
From thermodynamics, we know energy must be conserved (energy conservation). Conventional wisdom would say that momentum must also be conserved; however, I have begun to think this is solely a classical dynamics idea. I know in quantum mechanics, the transfer of momentum is also conserved, but when I try to correlate this with General Relativity's view of the world in terms of the stress-energy tensor, I find that momentum flux (and thus in my mind, momentum) is merely a product of an energy density. After all, if mass is just energy in the form of mass-energy, why can't this mass-energy move thus making momentum? It would seem to me that the so-called "conservation of momentum" is just another way of saying "energy is conserved" in a different way.
In the Shawyer drive, energy is conserved: you still have to provide energy to the system, and in return you get thrust. If momentum is truly just another form of energy, why do skeptics think this can't work?
So to be succinct (sorry, that was long-winded), why is the momentum conservation law so important if everything boils down to energy at the end of the day? If everything (and I mean everything) truly is just different forms of energy, shouldn't it be obvious that it must be possible to convert it from one form to another via some pathway or process?
Thanks in advance for helping me with my little thought!